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The predictive current control algorithm of permanent magnet synchronous motor (PMSM) drives has precise current tracking, constant switching frequency and is suitable for digital implementation. However, the conventional deadbeat predictive current control algorithm is sensitive to the stator inductance parameter mismatch. This paper presents an improved deadbeat predictive current control algorithm while achieving significantly increased robustness to inductance parameter mismatch. The current offset constraint and output voltage prediction method were modified. The relationship between system stability and inductance mismatch was analyzed using root locus method. In addition, the proposed algorithm is very simple and can be effectively implemented. Simulation results demonstrate the effectiveness of the proposed predictive current control algorithm. The system robustness is proven.